Some Haskell Functions on Polynomials

HaskellCalculus.hs

module Main where

type Zahlen = Float
data Term degree coefficient = Term Zahlen Zahlen deriving (Show, Eq)
type Polynomial = [Term Zahlen Zahlen]

zeroPolynomial = Term 0 0

pDerive (Term 0 n) = zeroPolynomial
pDerive (Term d n) = Term (d - 1) (n * d)

pIntegrate (Term d n) = Term (d + 1) (n / (d + 1))

derive :: Polynomial -> Polynomial
derive ps = map pDerive ps

integrate :: Polynomial -> (Zahlen -> Polynomial)
integrate ps = (\k -> (map pIntegrate ps) ++ (makePolynomial 0 k))

evalTerm x (Term 0 n) = n
evalTerm x (Term d n) = n*(x**d)

evalPoly x ps = foldl (+) 0 $ map (evalTerm x) ps

makePolynomial d n = [Term d n]


main = putStrLn $ show $ evalPoly 10 $ ( integrate (makePolynomial 2 1) 10 )